An example pertaining to the failure of the Besicovitch-Federer structure theorem in Hilbert space
| Autor: | Thierry De Pauw |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Hilbert manifold
28A80 General Mathematics Mathematics::General Topology 53C65 Rectifiable set purely unrectifiable set Hilbert space Negligible set Cylinder set measure 01 natural sciences Null set symbols.namesake 0103 physical sciences Mathematics::Metric Geometry 0101 mathematics Mathematics Discrete mathematics 010102 general mathematics Rigged Hilbert space Mathematics::Logic Set function symbols Purely unrectifiable set 28A75 010307 mathematical physics Borel set Reproducing kernel Hilbert space |
| Zdroj: | Recercat. Dipósit de la Recerca de Catalunya instname Publ. Mat. 61, no. 1 (2017), 153-173 Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Publicacions Matemàtiques; Vol. 61, Núm. 1 (2017); p. 153-173 |
| Popis: | We give an example, in the infinite dimensional separable Hilbert space, of a purely unrectifiable Borel set with finite nonzero one dimensional Hausdorff measure, whose projection is nonnegligible in a set of directions which is not Aronszajn null. |
| Databáze: | OpenAIRE |
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